Recursive functionals and quantifiers of finite types revisited. V

Author:
S. C. Kleene

Journal:
Trans. Amer. Math. Soc. **325** (1991), 593-630

MSC:
Primary 03D65

DOI:
https://doi.org/10.1090/S0002-9947-1991-0974519-8

MathSciNet review:
974519

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Abstract: This is the last in a sequence of papers that redoes the theory of recursion in finite types. A key feature of the theory is that a computation can succeed (or finish) even if some of its subcomputations do not, if these turn out to be irrelevant to the total computation. I give a detailed description of computations involving oracles for type functionals. The computation may be viewed formally as a transfinite sequence of symbolic expressions, but I also describe a semantics in which each expression is given a concrete realization.

**[1978**Generalized Recursion Theory, II, Proceedings of the 1977 Oslo Symposium (June 13-17) (J. E. Fenstad, R. O. Gandy, and G. E. Sacks, eds.), North-Holland, Amsterdam, pp. 185-222. MR*Recursive functionals and quantifiers of finite types revisited*, I]**516936 (80k:03048)****[1980**, June 18-24, 1978) (J. Barwise, H. J. Keisler, and K. Kunen, eds.), North-Holland, Amsterdam, pp. 1-29. MR*Recursive functionals and quantifiers of finite types revisited*, II, The Kleene Symposium (Madison, Wis]**591873 (83j:03076)****[1982**Metakides, ed.), North-Holland, Amsterdam, pp. 1-40. MR*Recursive functionals and quantifiers of finite types revisited*, III, Patras Logic Symposion (Patras, Greece, August 18-22, 1980) (G]**694251 (84g:03071)****[1985**Sympos. Pure Math, (from the American Mathematical Society's 1982 Summer Research Institute on Recursion Theory at Cornell University, June 27-July 16) (A. Nerode, ed.), vol. 42, Amer. Math. Soc., Providence, R.I., pp. 119-138.*Unimonotone functions of finite types*(*Recursive functionals and quantifiers of finite types revisited*, IV), Proc]

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DOI:
https://doi.org/10.1090/S0002-9947-1991-0974519-8

Article copyright:
© Copyright 1991
American Mathematical Society